Lévy Processes

This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.

Jean Bertoin (Author)

9780521646321, Cambridge University Press

Paperback, published 29 October 1998

278 pages
22.9 x 15.2 x 1.6 cm, 0.41 kg

' … this concise book promises to be the standard reference for students and researchers concerned with this field.' International Mathematical News

This 1996 book is a comprehensive account of the theory of Lévy processes. This branch of modern probability theory has been developed over recent years and has many applications in such areas as queues, mathematical finance and risk estimation. Professor Bertoin has used the powerful interplay between the probabilistic structure (independence and stationarity of the increments) and analytic tools (especially Fourier and Laplace transforms) to give a quick and concise treatment of the core theory, with the minimum of technical requirements. Special properties of subordinators are developed and then appear as key features in the study of the local times of real-valued Lévy processes and in fluctuation theory. Lévy processes with no positive jumps receive special attention, as do stable processes. In sum, this will become the standard reference on the subject for all working probability theorists.

Preliminaries
1. Lévy processes as Markov processes
2. Elements of potential theory
3. Subordinators
4. Local time and excursions of a Markov process
5. Local times of a Lévy process
6. Fluctuation theory
7. Lévy processes with no positive jumps
8. Stable processes and the scaling property
Bibliography
Glossary
Index.

Subject Areas: Calculus & mathematical analysis [PBK]